There are two basic grounds for appealing dismissal really. Either you think dismissing you wasn't a reasonable decision, or you think they didn't dismiss you in a fair, lawful way. (Or both).
Depending on which it is, say, for example, you are appealing your dismissal because you do not think dismissal was a reasonable decision in the circumstances, and explain why you think that. Or, you do not feel they followed a fair and reasonable procedure and give the reasons why you think that; what was wrong with the procedure they used.
I agree with Flowery a bit more information would be helpful. Making an appeal against a dismissal needs to document why you feel it was unfair. If you can you need to make reference to the company policy and procedures and if you find that they did not follow them in anyway leading up to your dismissal then this could be deemed unfair and this is what you could base your appeal on quoting any relevant chapters of their own documents.